Details

sample65.0ms

Algorithm

intervals

Results

24.0ms	83×	body	1280	valid
14.0ms	74×	body	10240	exit
7.0ms	42×	body	640	valid
3.0ms	87×	body	80	valid
3.0ms	24×	body	320	valid
2.0ms	20×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	8	7
done	8	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
5.8b	(- (exp x) 1.0)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 67

Calls

2 calls:

49.0ms	(/ (exp x) (- (exp x) 1.0))
25.0ms	(- (exp x) 1.0)

series64.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (exp x) (- (exp x) 1.0))
16.0ms	(- (exp x) 1.0)

simplify868.0ms

Counts

73 → 73

Iterations

Useful iterations: done (864.0ms)

Iter	Nodes	Cost
0	117	900
1	254	793
2	896	708
done	5000	690

prune275.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/12 x (/ 1 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 1/12 x (/ 1 x))

series76.0ms

Counts

1 → 3

Calls

1 calls:

76.0ms

(fma 1/12 x (/ 1 x))

simplify1.6s

Counts

13 → 13

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	16	108
1	24	105
2	70	93
3	280	93
4	1370	93
done	5000	93

prune45.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma 1/12 x (/ 1 x)))
0.1b	(fma 1/12 x (/ 1 x))
0.1b	(fma 1/12 x (/ 1 x))
0.2b	(* (sqrt (fma 1/12 x (/ 1 x))) (sqrt (fma 1/12 x (/ 1 x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`fma-udef`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

1.0ms	(sqrt (fma 1/12 x (/ 1 x)))
0.0ms	(fma 1/12 x (/ 1 x))
0.0ms	(fma 1/12 x (/ 1 x))
18.0ms	(* (sqrt (fma 1/12 x (/ 1 x))) (sqrt (fma 1/12 x (/ 1 x))))

series227.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (fma 1/12 x (/ 1 x)))
73.0ms	(fma 1/12 x (/ 1 x))
59.0ms	(fma 1/12 x (/ 1 x))
51.0ms	(* (sqrt (fma 1/12 x (/ 1 x))) (sqrt (fma 1/12 x (/ 1 x))))

simplify1.3s

Counts

98 → 98

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	80	1388
1	178	937
2	902	827
done	5000	804

prune282.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/12 x (/ 1 x))
0.1b	(fma 1/12 x (/ 1 x))
0.1b	(* (pow (sqrt (sqrt (fma 1/12 x (/ 1 x)))) 3) (sqrt (sqrt (fma 1/12 x (/ 1 x)))))
0.3b	(pow (sqrt (sqrt (fma 1/12 x (/ 1 x)))) 3)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

87×	`sqrt-prod`
66×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
24×	`associate-l` `unswap-sqr`
21×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`associate-r`
8×	`pow1`
7×	`add-cbrt-cube`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `pow1/2` `unpow3` `pow-exp` `fma-udef`
1×	`pow-plus` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 135

Calls

4 calls:

1.0ms	(fma 1/12 x (/ 1 x))
1.0ms	(fma 1/12 x (/ 1 x))
59.0ms	(* (pow (sqrt (sqrt (fma 1/12 x (/ 1 x)))) 3) (sqrt (sqrt (fma 1/12 x (/ 1 x)))))
17.0ms	(pow (sqrt (sqrt (fma 1/12 x (/ 1 x)))) 3)

series395.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma 1/12 x (/ 1 x))
56.0ms	(fma 1/12 x (/ 1 x))
64.0ms	(* (pow (sqrt (sqrt (fma 1/12 x (/ 1 x)))) 3) (sqrt (sqrt (fma 1/12 x (/ 1 x)))))
213.0ms	(pow (sqrt (sqrt (fma 1/12 x (/ 1 x)))) 3)

simplify1.6s

Counts

147 → 147

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	152	3080
1	429	2265
2	1920	2119
done	5001	1858

prune419.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes102.0ms

Accuracy

98.2% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 21.1b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	29
1	24	29
done	24	29

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	2503×	body	10240	exit
737.0ms	2290×	body	1280	valid
412.0ms	1663×	body	640	valid
105.0ms	2805×	body	80	valid
105.0ms	804×	body	320	valid
41.0ms	440×	body	160	valid